Q: What are the factor combinations of the number 43,542,121?

 A:
Positive:   1 x 435421217 x 6220303109 x 399469149 x 292229383 x 113687763 x 570671043 x 417472681 x 16241
Negative: -1 x -43542121-7 x -6220303-109 x -399469-149 x -292229-383 x -113687-763 x -57067-1043 x -41747-2681 x -16241


How do I find the factor combinations of the number 43,542,121?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 43,542,121, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 43,542,121
-1 -43,542,121

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 43,542,121.

Example:
1 x 43,542,121 = 43,542,121
and
-1 x -43,542,121 = 43,542,121
Notice both answers equal 43,542,121

With that explanation out of the way, let's continue. Next, we take the number 43,542,121 and divide it by 2:

43,542,121 ÷ 2 = 21,771,060.5

If the quotient is a whole number, then 2 and 21,771,060.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 43,542,121
-1 -43,542,121

Now, we try dividing 43,542,121 by 3:

43,542,121 ÷ 3 = 14,514,040.3333

If the quotient is a whole number, then 3 and 14,514,040.3333 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 43,542,121
-1 -43,542,121

Let's try dividing by 4:

43,542,121 ÷ 4 = 10,885,530.25

If the quotient is a whole number, then 4 and 10,885,530.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 43,542,121
-1 43,542,121
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

171091493837631,0432,68116,24141,74757,067113,687292,229399,4696,220,30343,542,121
-1-7-109-149-383-763-1,043-2,681-16,241-41,747-57,067-113,687-292,229-399,469-6,220,303-43,542,121

More Examples

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